Answer:
48 minutes
Explanation:
We will use the equation d=rt for this situation, where d is distance, r is the rate of speed and t is the time.
Let r be Max's rate of speed and t be the total time.
With both on hoverboards, Victoria is 3 times as fast as Max; this would be represented as 3r. She travels at this speed for 12 minutes; this gives us the expression 3r(12).
For the remainder of the race, Victoria is 3 times slower than Max. This is represented as 1/3r. We do not know the amount of time she travels this way; we will represent this as 1/3r(t-12), since t is the total time and she has already spent 12 minutes on the hoverboard.
Together the distance on hoverboard and the distance on foot can be represented by d=3r(12)+1/3r(t-12).
This is the same distance that Max travels. Max's distance is represented using the equation d=rt. Setting them equal, we have
3r(12)+1/3r(t-12) = rt
Simplifying, we have
36r+1/3r(t)-1/3r(12) = rt
36r + 1/3rt - 12/3r = rt
36r + 1/3rt - 4r = rt
Combining like terms,
32r + 1/3rt = rt
Subtract 1/3rt from each side:
32r + 1/3rt - 1/3rt = rt - 1/3rt
32r = 2/3rt
Divide both sides by r:
32r/r = (2/3rt)/r
32 = 2/3t
Divide both sides by 2/3:
32 ÷ 2/3 = 2/3t ÷ 2/3
32 ÷ 2/3 = t
32/1 × 3/2 = t
96/2 = t
48 = t